Velocity Verlet algorithm - Revision history

Carl McBride: /* References */ Added a recent publication

2018-05-03T09:46:11Z

References: Added a recent publication

← Older revision		Revision as of 11:46, 3 May 2018
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	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1063/1.442716 William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics '''76''' pp. 637-649 (1982)]		*[http://dx.doi.org/10.1063/1.442716 William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics '''76''' pp. 637-649 (1982)]
			*[https://doi.org/10.1063/1.5008438 Jaewoon Jung, Chigusa Kobayashi, and Yuji Sugita "Kinetic energy definition in velocity Verlet integration for accurate pressure evaluation", Journal of Chemical Physics '''148''' 164109 (2018)]

	==External resources==		==External resources==
	*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.04 Velocity version of Verlet algorithm ] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].		*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.04 Velocity version of Verlet algorithm ] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].
	[[category: Molecular dynamics]]		[[category: Molecular dynamics]]

Nice and Tidy: Changed references to Cite format and added internal link

2010-11-26T09:20:31Z

Changed references to Cite format and added internal link

← Older revision		Revision as of 11:20, 26 November 2010
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	The '''Velocity Verlet algorithm''' for use in [[molecular dynamics]] is given by		The '''Velocity Verlet algorithm''', for use in [[molecular dynamics]], is given by <ref>[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98-103 (1967)]</ref>:

	:<math>r(t + \delta t) = r (t) + \delta t v(t) + \frac{1}{2} \delta t^2 a(t)</math>		:<math>r(t + \delta t) = r (t) + \delta t v(t) + \frac{1}{2} \delta t^2 a(t)</math>
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	:<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math>		:<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math>

	where <math>r</math> is the position, <math>v</math> is the velocity, <math>a</math> is the acceleration and <math>t</math> is the time.		where <math>r</math> is the position, <math>v</math> is the velocity, <math>a</math> is the acceleration and <math>t</math> is the time. <math>\delta t</math> is known as the [[time step]].
	==See also==		==See also==
	*[[Verlet leap-frog algorithm]]		*[[Verlet leap-frog algorithm]]
	==References==		==References==
	~~#[http:~~/~~/dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review~~ '''~~159~~''' ~~pp. 98-103 (1967)]~~		<references/>
	#[http://dx.doi.org/10.1063/1.442716 William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics '''76''' pp. 637-649 (1982)]		'''Related reading'''
			*[http://dx.doi.org/10.1063/1.442716 William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics '''76''' pp. 637-649 (1982)]
	==External resources==		==External resources==
	*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.04 Velocity version of Verlet algorithm ] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].		*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.04 Velocity version of Verlet algorithm ] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].
	[[category: Molecular dynamics]]		[[category: Molecular dynamics]]

152.78.97.17: added "a is the acceleration" for the equation

2010-11-26T08:00:33Z

added "a is the acceleration" for the equation

← Older revision		Revision as of 10:00, 26 November 2010
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	:<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math>		:<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math>

	where <math>r</math> is the position, <math>v</math> is the velocity and <math>t</math> is the time.		where <math>r</math> is the position, <math>v</math> is the velocity, <math>a</math> is the acceleration and <math>t</math> is the time.
	==See also==		==See also==
	*[[Verlet leap-frog algorithm]]		*[[Verlet leap-frog algorithm]]

Nice and Tidy: Added link to code F.04

2009-02-08T17:10:20Z

Added link to code F.04

← Older revision		Revision as of 19:10, 8 February 2009
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			The '''Velocity Verlet algorithm''' for use in [[molecular dynamics]] is given by

	:<math>r(t + \delta t) = r (t) + \delta t v(t) + \frac{1}{2} \delta t^2 a(t)</math>		:<math>r(t + \delta t) = r (t) + \delta t v(t) + \frac{1}{2} \delta t^2 a(t)</math>

	:<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math>		:<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math>

			where <math>r</math> is the position, <math>v</math> is the velocity and <math>t</math> is the time.
	==See also==		==See also==
	*[[Verlet leap-frog algorithm]]		*[[Verlet leap-frog algorithm]]
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	#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98-103 (1967)]		#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98-103 (1967)]
	#[http://dx.doi.org/10.1063/1.442716 William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics '''76''' pp. 637-649 (1982)]		#[http://dx.doi.org/10.1063/1.442716 William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics '''76''' pp. 637-649 (1982)]
			==External resources==
			*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.04 Velocity version of Verlet algorithm ] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].
	[[category: Molecular dynamics]]		[[category: Molecular dynamics]]

Carl McBride at 14:44, 23 September 2007

2007-09-23T14:44:58Z

← Older revision		Revision as of 16:44, 23 September 2007
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	:<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math>		:<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math>
			==See also==
			*[[Verlet leap-frog algorithm]]
	==References==		==References==
	#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98 - 103 (1967)]		#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98-103 (1967)]
	#[http://dx.doi.org/10.1063/1.442716 William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics '''76''' pp. 637-649 (1982)]		#[http://dx.doi.org/10.1063/1.442716 William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics '''76''' pp. 637-649 (1982)]
	[[category: Molecular dynamics]]		[[category: Molecular dynamics]]

Carl McBride: New page: : $r(t + \delta t) = r (t) + \delta t v(t) + \frac{1}{2} \delta t^2 a(t)$ : $v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]$ ==Refer...

2007-06-15T10:59:03Z

New page: :<math>r(t + \delta t) = r (t) + \delta t v(t) + \frac{1}{2} \delta t^2 a(t)</math> :<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math> ==Refer...

New page

:<math>r(t + \delta t) = r (t) + \delta t v(t) + \frac{1}{2} \delta t^2 a(t)</math>

:<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math>
==References==
#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98 - 103 (1967)]
#[http://dx.doi.org/10.1063/1.442716 William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics '''76''' pp. 637-649 (1982)]
[[category: Molecular dynamics]]